Humans are the only race that can learn Dual Wield, so they're basically the best Melee race by default. Get Luso Dual Wield ASAP and make him a Paladin with Fighter subclass and he will absolutely wreck shit. He'll do ridiculous amounts of damage and take almost none in return. On the magic side, humans are the only ones that can become Blue Mages or Seers, but you don't unlock Seers until really late. I just did the quest that unlocked the class a few minutes ago and I'm over 40 hours in. Blue Mages also aren't terribly useful until you have a Beastmaster that can control all of the enemy monsters and get them to use their most useful abilities on the person with Learn, so that you can get them reliably to use yourself. Really, the later human jobs are much better than the early ones.
Bangaa and Viera are definitely the most varied races, and Nu Mou are good at what they do (magic) and pretty much nothing else. To be honest, the Nu Mou have kind of disappointed me because their good abilities are spread out between all of their classes so it's difficult to get a build that I feel maxes out their potential. I have mine as a Time Mage with a Black Mage subclass right now, because Haste and Stop are damn useful, but that way I'm limited to fire/ice/lightning attack spells. I only have one Gria so far and I haven't even unlocked all of their classes yet, so I can't really assess how good they are at this point.
The two races I don't think are very good at all are Moogles and Seeqs. Gunners aren't nearly as useful anymore, because maps are bigger now, they do less damage, and the status effects seem to trigger less often. The flintlock class I think kind of sucks, because they need to take a turn to prime before they can even use any of their abilities, their curative ability isn't nearly as useful as a dedicated healer, and their abilities cannot be used as a subclass because they require the handcannon weapon equipped to use. Everything else is just inferior to other races. Seeqs only have four classes, three of which are done better by other races, and the fourth (Ranger) is a gimmick because using traps against your enemy is based almost entirely on luck.
Basically, my opinions on optimal races for archetypes:
Melee: Human (aforementioned Paladin/Fighter with Dual Wield), Bangaa (Templar/Dragoon or Master Monk/something else), and maybe Gria (don't know for sure until I unlock Raptor)
Long-range Attacker: Viera (Assassin/Sniper), Bangaa (Cannoneer/Trickster), and maybe Gria (Hunter/Geomancer, but I haven't unlocked the latter so I don't know how useful those abilities are)
Healer: Viera (White Mage is the most obvious, of course, but Elementalists and Summoners have healing abilities as well, and you can choose almost anything as the second class)
Attack Mage: Nu Mou (any two except Arcanist and Illusionist, those kind of suck imo), Viera (Elementalist/Summoner, not as good for damage but great damage/status effect spells for very little MP), maybe Humans depending on how good the Seer class is
Support Magic: Nu Mou (Time Mage/something), Viera (Green Mage/something)
When you want to get into hybrid classes, you can obviously experiment a lot more. In terms of useful classes to crappy classes, I agree that Viera are the best, although Bangaa are a close second. However, Humans are really the best melee race, because nobody else can dual wield, and Paladins have great stat growths for dealing and taking damage. I'm sort of iffy on Nu Mou, and I can't really gauge Gria yet, but I will definitely suggest staying away from Moogles and Seeqs, because they aren't worth the trouble.
